The origins of the fundamental theorem of surface theory
type: Item
instance of: scholarly article
title: The origins of the fundamental theorem of surface theory
zbMATH Open document ID: 1505.01037
author: Alberto Cogliati
author: Rachele Rivis
published in: Historia Mathematica
publication date: 2022-12-08T00:00:00Z
review text: The paper traces the history of two related results in classical differential geometry, namely the Mainardi-Codazzi equations, which provide relations between the first and the second fundamental form, and the fundamental theorem of surface theory, which guarantees the existence and uniqueness (up to rigid motions) of a surface with prescribed first and second fundamental form. Both results are closely linked to the Grand Prix des Mathématiques announced by the Académie des Sciences de Paris in 1859, which focused on the problems of applicability of surfaces (where the term ``applicable'' is understood as ``locally isometric''). The present paper provides a detailed overview and comparison between the prize memoirs of Edmond Bour (who received the prize), Ossian Bonnet and Delfino Codazzi (who both received an honorable mention). It also traces some subsequent developments, in particular Bonnet's 1867 proof of the fundamental theorem.
reviewed by: Antonín Slavík
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 53-03
Mathematics Subject Classification ID: 53A05
zbMATH DE Number: 7629767
zbMATH Keywords: surface theory
zbMATH Keywords: applicability problem
zbMATH Keywords: fundamental theorem of surface theory
zbMATH Keywords: Mainardi-Codazzi equations
zbMATH Keywords: Grand Prix des Mathématiques
MaRDI profile type: Publication
full work available at URL: j.hm.2022.09.001
OpenAlex ID: W4308403714
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cites work: Q3169192
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DOI: 10.1016/J.HM.2022.09.001
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description: scientific article; zbMATH DE number 7629767